The former Labour Prime Minister is under pressure to approve the release of what could be the only independent record of a conversation in which he allegedly declared war on Mr Murdoch.

Asked by a Tory MP if Mr Cameron should agree that Downing Street phone records should be published between Mr Brown and Mr Murdoch, Mr Cameron replied: “Governments cannot release information provided by previous administrations but I am sure this is an issue that the previous Prime Minister will want to consider given the very clear statement that he made.”

The former Labour Prime Minister had told the Leveson inquiry into press ethics this week that he had never threatened Mr Murdoch in the phone call to discuss The Sun newspaper’s coverage of the war in Afghanistan in November 2009.

This directly contradicted separate evidence from Mr Murdoch, who had said that Mr Brown had told him his Government was at “war” with News International.

Mr Brown’s spokesman declined to respond to questions from The Daily Telegraph on Wednesday.